Recover a true base rate when the noise rates are known

Inverts \(p_{obs} = p(1-\beta) + (1-p)\alpha\) (Research.P5.trueRate_observedRate).

Usage

morie_fairness_true_rate(p_obs, alpha, beta)

Arguments

p_obs

Recorded (proxy) base rate, one or more values in [0, 1].

alpha, beta

Known noise rates with alpha + beta < 1.

Value

The true base rate(s).

Examples

p <- 0.4
p_obs <- p * (1 - 0.2) + (1 - p) * 0.1
morie_fairness_true_rate(p_obs, alpha = 0.1, beta = 0.2)   # 0.4
#> [1] 0.4